World of Polyhedra - Enumeration of a polyhedral subset

Enumeration of a polyhedral subset

This work demonstrates an enumeration of a polyhedral subset. A polyhedron is belong to the subset if all its vertex is constituted or surrounded by same combination of regular polygons, while the permutation of polygons is not concerned.
For example, for the polyhedron [3.3.4.4..2] in subset, its vertex is constituted by 1 combination of (3,3,4,4), but 2 permutation, (3,3,4,4) and (3,4,3,4).

Created : 2003-5-23 16:36:13 Last Modified : 2003-9-14 18:31:57

Enumerating program
Download: phcalcu.zip
This is a ployhedra enumerating program.
Run on windows 9x/NT/2000/XP

Press "all" and get the result.
In author's P4 1.6G 256M DDR, it's need about 4 seconds.
- Flowchart
Enumerating Result
The enumerating result can be grouped with 3 kinds.
- Platonic Polyhedra
  The Platonic Solids, discovered by the Pythagoreans but described by Plato (in the Timaeus) and used by him for his theory of the 4 elements, consist of surfaces of a single kind of regular polygon, with identical vertices.
- Archimedean Polyhedra
  The Archimedean Solids, consist of surfaces of more than a single kind of regular polygon, with identical vertices and identical arrangements of polygons around each polygon.
- Archimedean Polyhedra Extended
  The vertexes of these polyhedra are constituted or surrounded by same combination of regular polygons, but the permutation of the polygons are more than one kind.